Photo-mask and wafer image reconstruction

ABSTRACT

A system receives a mask pattern and a first image of at least a portion of a photo-mask corresponding to the mask pattern. The system determines a second image of at least the portion of the photo-mask based on the first image and the mask pattern. This second image is characterized by additional spatial frequencies than the first image.

RELATED APPLICATIONS

This application is a continuation of U.S. Nonprovisional patentapplication Ser. No. 12/440,722, filed Feb. 5, 2010, which is a U.S.national phase application under 35 U.S.C. §371 of International PatentApplication No. PCT/US2007/078913 filed Sep. 19, 2007, which claims thebenefit of and priority to U.S. provisional application Ser. No.60/826,294 filed Sep. 20, 2006, which are each incorporated herein byreference.

This application is related to the following copending patentapplications: application Ser. No. 12/475,331; application Ser. No.12/475,349; application Ser. No. 12/475,354; application Ser. No.12/475,361, and application Ser. No. 12/475,369, all of which were filedconcurrently herewith, which are each incorporated herein by reference.

BACKGROUND

1. Field of the Invention

The present invention relates to techniques for processing images. Morespecifically, the invention relates to reconstruction of photo-mask andwafer images.

2. Related Art

Photolithography is a widely used technology for producing integratedcircuits. In this technique, a light source illuminates a photo-mask.The resulting spatially varying light pattern is projected on to aphotoresist layer on a semiconductor wafer by an optical system(referred to as an exposure tool). By developing the 3-dimensionalpattern produced in this photoresist layer, a layer in the integratedcircuit is created. Furthermore, since there are often multiple layersin a typical integrated circuit, these operations may be repeated usingseveral photo-masks to produce a product wafer.

Unfortunately, as dimensions in integrated circuits steadily become asmaller fraction of the wavelength of the light used to expose images ofthe photo-mask onto the wafer, the structures in or on the idealphoto-mask (also referred to as the mask pattern) and/or the physicalstructures in or on the actual photo-mask bear less and less resemblanceto the desired or target pattern at the wafer. These differences betweenthe mask pattern and the target pattern are used to compensate for thediffraction and proximity effects that occur when light is transmittedthrough the optics of the exposure tool and is converted into the3-dimensional pattern in the photoresist.

From a photo-mask or reticle manufacturing standpoint, the increasingdissimilarity between the photo-mask and the corresponding waferpatterns creates a broad new class of problems in photo-mask inspectionand qualification. For example, if a defect in a photo-mask is detected,it is often unclear what impact this defect will have on the finalpattern in the photoresist. In addition, photo-mask inspection devicesoften have a different numerical aperture, different illuminationconfiguration, and even different light wavelength(s) than those used inthe wafer exposure tool. As a consequence, the image measured by aphoto-mask inspection tool is often neither a perfect replica of thephysical photo-mask or the pattern that will be exposed onto the wafer.

One existing approach to the former challenge uses a computer tosimulate the resulting wafer pattern based on the inspection images ofthe photo-mask. By comparing simulations of wafer patterns correspondingto the ideal photo-mask (i.e., the target mask pattern) and an estimateof the actual photo-mask corresponding to the image of the photo-mask,the significance of the defect may be determined. However, since theimage of the photo-mask may not be an accurate representation of theactual photo-mask, errors may be introduced when simulating waferpatterns, and thus, when trying to identify or classify defects. Thismay further complicate photo-mask inspection and qualification.

Similar issues arise when inspecting the patterned wafers. Hence, whatis needed are photo-mask and patterned wafer inspection techniques thatovercome the problems listed above.

SUMMARY

One embodiment of the present invention provides a computer system fordetermining an image. The system receives a mask pattern and a firstimage of at least a portion of a photo-mask corresponding to the maskpattern. The system determines a second image of at least the portion ofthe photo-mask based on the first image and the mask pattern. Thissecond image is characterized by additional spatial frequencies than thefirst image.

In some embodiments, the mask pattern is characterized by spatialfrequencies within a first band of frequencies, the first image ischaracterized by spatial frequencies within a second band of frequenciesthat is less than the first band of frequencies, and the second image ischaracterized by spatial frequencies within a third band of frequenciesthat is greater than the second band of frequencies. The third band offrequencies may approximately include the first band of frequencies.

In some embodiments, the system identifies features in the second imagecorresponding to differences between at least the portion of thephoto-mask and the mask pattern (such as defects in the photo-mask).Furthermore, the system may determine an acceptance condition of thephoto-mask based on at least a subset of the features and/or a number ofthe features in at least the subset of the features.

In some embodiments, at least the subset of the features is identifiedby the system based on an estimated pattern that results from aphotolithographic process using an estimated photo-mask that correspondsto the second image. The estimated pattern may be calculated using amodel of an optical path used in the photolithographic process. Forexample, the model of the optical path may include a forward opticalcalculation in which the estimated photo-mask is included in an objectplane to determine the estimated pattern. In addition, the estimatedpattern may be calculated using a model of a photoresist used in thephotolithographic process. And in some embodiments, at least the subsetof the features may be further identified by the system based ondifferences between the estimated pattern and a target pattern thatcorresponds to at least a portion of an integrated circuit.

In some embodiments, the acceptance condition of the photo-mask is basedon a process window corresponding to the estimated photo-mask and/orbased on features identified throughout the process window.

In some embodiments, at least the subset of the features is identifiedbased on a set of pre-determined features and/or statistical propertiesof the set of pre-determined features, Furthermore, in some embodimentsthe system provides a ranking of at least the subset of the features.

In some embodiments, the system iteratively performs the operations ofdetermining the second images and identifying the features, where atleast the subset of the features identified have a likelihood ofoccurrence exceeding a pre-determined value.

In some embodiments, the second image is determined using an inverseoptical calculation in which the first image is in an image plane of amodel of an optical path that corresponds to an optical inspectiondevice used to generate the first image and the second image is in anobject plane of the model of the optical path.

In some embodiments, the second image is further determined based on athird image of the photo-mask, where the first image and the third imagecorrespond to different focal surfaces in the optical inspection device.Furthermore, the second image may be determined based on weights for thefirst image and the third image, and/or the first image and the thirdimage may include magnitude and phase information.

In another embodiment, the system receives the mask pattern and thefirst image. The system determines the second image based on the firstimage and the mask pattern in an optical calculation that uses the modelof the optical path corresponding to the optical inspection device inwhich the first image is included in an image plane and the second imageis included in an object plane. This second image is characterized byadditional spatial frequencies than the first image.

The determining may include an iterative calculation and/or may be inaccordance with a gradient descent calculation (for example, using asteepest descent technique).

In yet another embodiment, the system receives a target pattern and afourth image of at least the portion of a patterned wafer correspondingto the target pattern. The system determines a fifth image of at leastthe portion of the patterned wafer based on the fourth image and thetarget pattern. This fifth image is characterized by additional spatialfrequencies than the fourth image.

Another embodiment provides a method including at least some of theabove-described operations.

Another embodiment provides a computer program product for use inconjunction with the computer system.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 is a block diagram illustrating an existing photo-mask inspectionsystem.

FIG. 2A is a block diagram illustrating a photo-mask inspection systemin accordance with an embodiment of the present invention.

FIG. 2B is a block diagram illustrating a photo-mask inspection systemin accordance with an embodiment of the present invention.

FIG. 2C is a block diagram illustrating a photo-mask inspection systemin accordance with an embodiment of the present invention.

FIG. 3A is a block diagram illustrating an inverse optical calculationin accordance with an embodiment of the present invention.

FIG. 3B is a block diagram illustrating a forward optical calculation inaccordance with an embodiment of the present invention.

FIG. 4A is a block diagram illustrating a wafer inspection system inaccordance with an embodiment of the present invention.

FIG. 4B is a block diagram illustrating a wafer inspection system inaccordance with an embodiment of the present invention.

FIG. 5A is a flow chart illustrating a process for determining an imagein accordance with an embodiment of the present invention.

FIG. 5B is a flow chart illustrating a process for determining an imagein accordance with an embodiment of the present invention.

FIG. 6 is a block diagram illustrating a mask pattern and correspondinglevel-set functions in accordance with an embodiment of the presentinvention.

FIG. 7 is a block diagram illustrating a pre-processing image and apost-processing image in accordance with an embodiment of the presentinvention.

FIG. 8 is a block diagram illustrating a computer system in accordancewith an embodiment of the present invention.

FIG. 9 is a flow chart illustrating a process for determining an imagein accordance with an embodiment of the present invention.

FIG. 10 is a block diagram illustrating an image data structure inaccordance with an embodiment of the present invention.

FIG. 11 is a block diagram illustrating a feature data structure inaccordance with an embodiment of the present invention.

Note that like reference numerals refer to corresponding partsthroughout the drawings.

DETAILED DESCRIPTION

The following description is presented to enable any person skilled inthe art to make and use the invention, and is provided in the context ofa particular application and its requirements. Various modifications tothe disclosed embodiments will be readily apparent to those skilled inthe art, and the general principles defined herein may be applied toother embodiments and applications without departing from the spirit andscope of the present invention. Thus, the present invention is notintended to be limited to the embodiments shown, but is to be accordedthe widest scope consistent with the principles and features disclosedherein.

Embodiments of a computer system, a method, and a computer programproduct (i.e., software) for use with the computer system are described.These devices and processes may be used to determine an image, such asone corresponding to a photo-mask or a patterned wafer. In particular,an initial image of the photo-mask or patterned wafer that is obtainedusing a photo-mask or wafer optical-inspection device may be processedto determine a final image. Note that in some embodiments, at least twoinitial images are used to determine the final image. These images maybe measured at different wavelengths and/or on different focal surfacesin the photo-mask or wafer optical-inspection device. More generally,these images may be determined at different imaging conditions(including focus, wavelength, illumination type, and/or measurementtechnique). In addition, each of these images may include magnitude andphase information. In one embodiment, the determining includes anoptical calculation that uses a model of the optical path in thephoto-mask or wafer optical-inspection device in which the initial imageis included in an image plane (such as the focal plane) and the finalimage is included in an object plane.

The final image may correct the initial image for artifacts due to focalerrors and/or optical aberrations associated with the optical path inthe photo-mask or wafer optical-inspection device. In addition, thefinal image may recover information about the photo-mask or patternedwafer that was corrupted, distorted, and/or absent in the initial image.For example, the final image may include information (includingmagnitude and/or phase information) at spatial frequencies that were notpresent in the initial image due to a finite numerical aperture of theoptical path and/or other limitations in the photo-mask or waferoptical-inspection device. For images of the photo-mask, such imageprocessing may be based on at least a portion of the desired or targetmask pattern. And for images of the patterned wafer, the imageprocessing may be based on the at least a portion of a desired or targetpattern, which may correspond to at least a portion of an integratedcircuit (such as a physical layout of at least the portion of theintegrated circuit). Note that this target pattern and/or the targetmask pattern may correspond to a document that is compatible withGraphic Design System II (GDSII) and/or OASIS format.

In some embodiments, additional simulations and/or measurements are usedto determine wafer patterns that correspond to the photo-mask. Forexample, an estimated wafer pattern (also referred to as a simulatedwafer image) that results from a photolithographic process that uses anestimated photo-mask corresponding to the final image may be calculated.Note that the estimated photo-mask may be determined by applying one ormore thresholds to the final image. Furthermore, this estimated waferpattern may be compared to the target pattern, another estimated waferpattern that is determined using the (target) mask pattern, and/or ameasured pattern on a patterned wafer that is produced using thephoto-mask.

Furthermore, features in the final image may be identified. For imagesof the photo-mask, these features may correspond to differences betweenat least the portion of the photo-mask and the mask pattern (forexample, due to defects in and/or on the photo-mask). And for images ofthe patterned wafer, these features may correspond to differencesbetween the pattern on the wafer and the target pattern (for example,due to defects in and/or on the wafer). The photo-mask and/or the wafermay be accepted or rejected based on at least a subset of the features.

This image processing approach may be implemented as a stand-alonesoftware application, or as a program module or subroutine in anotherapplication, such as photo-mask and/or wafer inspection software.Furthermore, the software may be configured to execute on a client orlocal computer, such as a personal computer, a laptop computer, or otherdevice capable of manipulating computer readable data, or between two ormore computing systems over a network (such as the Internet, World WideWeb or WWW, Intranet, LAN, WAN, MAN, or combination of networks, orother technology enabling communication between computing systems).Therefore, information to be used when determining images may be storedlocally (for example, on the local computer) and/or remotely (forexample, on a computer or server that is accessed via a network).

We now describe embodiments of a computer system, a method, and softwarefor determining an image. FIG. 1 provides a block diagram illustratingan existing photo-mask inspection system 100. In the photo-maskinspection system 100, an optical-inspection device 112 (such as theTeraScan™ photo-mask inspection system from KLA-Tencor, Inc., of SanJose, Calif.) determines an inspection image 114 of a photo-mask 110.Note that throughout the following discussion the inspection image 114,as well as any of the other images (such as reconstructed images) and/orpatterns (such as mask patterns) described below, may be a bitmap orgrayscale file that includes a set of values corresponding to pixels inan image. Furthermore, the quantization (i.e., the number of bits) inthese image files may be varied, as needed, during the calculations thatare described. Alternative formats having the same or similarinformation content, including a vector-based format such as GDSII, maybe used in some embodiments of the images and/or patterns. And in someembodiments, the images include real and imaginary components (orequivalently, magnitude and phase information).

Using a lithography simulator 116, a simulated or estimated wafer image118 (i.e., an image of an estimated pattern that may be produced usingan estimated photo-mask that corresponds to the inspection image 114)may be determined. Furthermore, photo-mask qualifier 128 may analyze thesimulated wafer image 118 to determine if it is acceptable, i.e., ifdifferences with respect to a target pattern 130 and/or any defects thatare present are within acceptable bounds, such as a fraction of acritical dimension in the target pattern. (Note that the target pattern130 may correspond to at least a portion of an integrated circuit.) Ifyes, the photo-mask 110 may be accepted, and if not the photo-mask 110may be rejected, subject to rework, or subject to additionalqualification testing.

However, as noted previously, limitations in the optical-inspectiondevice 112 result in differences between the estimated photo-mask thatcorresponds to the inspection image 114 and the photo-mask 110. As aconsequence, analysis of the simulated wafer image 118 may not besufficient to determine if there are defects in the photo-mask 110and/or if defects that are detected are significant. Thus, thelimitations of the optical-inspection device 112 may gate the ability toqualify photo-masks, and may impact photo-mask and/or patterned waferyields.

Alternatively, the photo-mask 110 may be qualified based on comparisonsbetween the simulated wafer image 118 or the target pattern 130 andactual wafer patterns produced or generated using the photo-mask 110.For example, a wafer-exposure system 120 (i.e., a photolithographicexposure tool) may be used to produce a printed wafer 122 using thephoto-mask 110, and a printed wafer image 126 of the pattern on theprinted wafer 122 may be determined using wafer-imaging device 124 (suchas the PUMA™ patterned wafer-inspection platform from KLA-Tencor, Inc.,of San Jose, Calif.). However, this brute-force approach is oftenexpensive and time consuming. In addition, errors introduced in thephotolithographic process in the wafer-exposure system 120 may reducethe accuracy of the qualification decision made by the photo-maskqualifier 128.

FIGS. 2A-2C provide block diagrams illustrating photo-mask inspectionsystems 200, 230 and 250 in accordance with an embodiment of the presentinvention. In photo-mask inspection system 200, a reconstructioncalculator 210 may determine a reconstructed photo-mask image 214 (i.e.,a second image) based on a (target) mask pattern 212 and the inspectionimage 114 (i.e., a first image). (Note that in some embodiments,patterns, such as the mask pattern 212, may have a document or fileformat that is similar to or the same as that for images, such as thereconstructed photo-mask image 214.) The reconstructed photo-mask image214 may correct for deficiencies in the inspection image 114, such asdefocus, aberrations, and/or lost information due to limitations of theoptical-inspection device 112. Since the reconstructed photo-mask image214 is a more faithful or accurate representation of the information inthe photo-mask 110, the simulated wafer image 118 (based on an estimatedphoto-mask that corresponds to the reconstructed photo-mask image 214)may also be more accurate. As a consequence, the photo-mask qualifier128 may be able to make more accurate qualification decisions, i.e.,whether or not the photo-mask 110 is acceptable.

Note these qualification decisions may be based on comparisons betweenthe simulated wafer image 118 and a printed wafer image (on a differentwafer or die, or on the same wafer, such as the printed wafer image 126illustrated in FIG. 2A or simulated reference wafer image 264 in FIG.2C), comparisons between the simulated wafer image 118 and the targetpattern 130 (as illustrated in FIG. 2B), comparisons between thesimulated wafer image 118 and another simulated wafer imagecorresponding to the mask pattern 212, comparisons between thereconstructed photo-mask image 214 and another reconstructed photo-maskimage (on the same or a different photo-mask), and/or comparisonsbetween the mask pattern 212 and an estimated photo-mask correspondingto the reconstructed photo-mask image 214. For example, as illustratedin the photo-mask inspection system 250, comparisons may be made basedon a reference inspection image 260 of at least a portion of the same ora different photo-mask. (Note that this is sometimes referred to asdie-to-database inspection.) Using the reconstruction calculator 210and/or the lithography simulator 216, reconstructed reference photo-maskimage 262 and/or the simulated reference wafer image 264 may bedetermined. The reconstructed reference photo-mask image 262 and/or thesimulated reference wafer image 264 may then be used in qualifying (ornot) the photo-mask 110.

As discussed below with reference to FIG. 5, features in thereconstructed photo-mask image 214 may be identified based on thesecomparisons and the photo-mask 110 may be accepted (or not) based on atleast a subset of the identified features. For example, the photo-mask110 may be accepted or rejected based on a type, severity, and/or numberof features (such as 1, 2, 5, 10, 25, 50, 100, 250, 500, and/or 1000identified features per photo-mask) that are identified. In addition,the photo-mask 110 may be accepted or rejected based on an impact ofsuch features on yield. Note that these features may correspond todefects in the photo-mask 110.

In some embodiments, at least the subset of the features is identifiedbased on a set of pre-determined features (such as known defects) and/orstatistical properties of the set of pre-determined features (such astheir probabilities of occurrence). Furthermore, in some embodiments thephoto-mask 110 is accepted (or not) based on a process window (such as arange of exposure times, a depth of focus, a range of exposureintensities, and/or a normalized image log slope) for the estimatedphoto-mask corresponding to the reconstructed photo-mask image 214 thatis used in the lithography simulator 116. In addition, in someembodiments the photo-mask 110 is accepted (or not) based on featuresidentified over or throughout the process window, and/or based on animpact on a critical dimension across the process window.

In some embodiments the photo-mask inspection system 200, the photo-maskinspection system 2030, and/or the photo-mask inspection system 250include fewer or additional components, two or more components arecombined into a single component, and/or a position of one or morecomponents may be changed. For example, in some embodiments thelithography simulator 116 and the simulated wafer image 118 may beexcluded. In these embodiments, the photo-mask 110 may be accepted (ornot) based on comparisons of the reconstructed photo-mask image 214 andthe mask pattern 212. Note that the photo-mask inspection system 200and/or the photo-mask inspection system 230 may be used withchromium-on-glass photo-masks, alternating phase-shifting photo-masks,attenuating phase-shifting photo-masks, and/or multiple-exposurephoto-masks (i.e., where patterns printed using two or more photo-masksare combined to produce a desired pattern).

In an example embodiment, the reconstructed photo-mask image 214 isdetermined using an inverse optical calculation. This is illustrated inFIG. 3A, which provides is a block diagram of an inverse opticalcalculation 300 in accordance with an embodiment of the presentinvention. In the inverse optical calculation 300, a suitablyilluminated predicted input 310 (such as the reconstructed photo-maskimage 214) is determined using an optical path 312 having an output 314(such as the inspection image 114 in FIGS. 2A-2C) in one of its imageplanes. In particular,R=I⁻¹IM,where I is a forward optical path (described in FIG. 3B below), I⁻¹ isan inverse optical path operator, M is the actual (physical) photo-maskpattern, I is an optical path operator, and the application of I to M isthe inspection image or the printed-wafer image, and R is thereconstructed image. In the case of the photo-mask inspection systems200 (FIG. 2A), 230 (FIG. 2B) and 250 (FIG. 2C), the optical path 312corresponds to the optical-inspection device 112 (FIGS. 2A and 2B),while in the wafer inspection systems 400 and 430 (described below inFIGS. 4A and 4B), the optical path 312 corresponds to the wafer-imagingdevice 124 (FIGS. 4A and 4B). Furthermore, the optical path 312 mayinclude illumination and/or optical effects. Note that the inverseoptical calculation 300 is described further below with reference toFIG. 5.

As noted previously, the predicted input 310 may be characterized byadditional spatial frequencies than the output 314. Using the photo-maskinspection systems 200 (FIG. 2A), 230 (FIG. 2B) and 250 (FIG. 2C) as anillustration, the mask pattern 212 (FIGS. 2A-2C) may be characterized byspatial frequencies within a first band of frequencies, the inspectionimage 114 (FIGS. 2A-2C) may be characterized by spatial frequencieswithin a second band of frequencies that is less than the first band offrequencies, and the reconstructed photo-mask image 214 (FIGS. 2A-2C)may be characterized by spatial frequencies within a third band offrequencies that is greater than the second band of frequencies.Furthermore, the third band of frequencies may approximately include thefirst band of frequencies.

The inverse optical calculation 300 may utilize more than one output314. Using the photo-mask inspection systems 200 (FIG. 2A), 230 (FIG.2B) and 250 (FIG. 2C) as an illustration, two or more inspection images(such as the inspection image 114 in FIGS. 2A-2C) may be used in thereconstruction calculator 210 (FIGS. 2A-2C). For example, there may betwo inspection images that are each determined using differentwavelengths, different focal conditions (i.e., on different focalsurfaces or planes), and/or different imaging conditions in the opticalinspection device 112 (FIGS. 2A-2C). These inspection images may includeintensity, magnitude and/or phase information. For example, images thatinclude magnitude and relative phase information may be measured bygenerating an interference pattern using measurement and reference beamsderived from a common light source or that are spatially and temporallycoherent. Alternatively, phase contrast optics may be utilized. In someembodiments, the difference of two inspection images may be used as theoutput 314 in the inverse optical calculation 300. Furthermore, in someembodiments each of the inspection images used in the inverse opticalcalculation 300 or a term(s) including some combination of theinspection images may be multiplied by a corresponding weight. In thisway, the calculation (and thus, the results) may emphasize one or moreof the inspection images relative to other inspection images used in theinverse optical calculation 300.

In another example embodiment, the simulated wafer image 118 (FIGS.2A-2C) is determined using a forward optical calculation. This isillustrated in FIG. 3B, which provides is a block diagram of a forwardoptical calculation 330 in accordance with an embodiment of the presentinvention. In the forward optical calculation 330, a predicted output344 (such as the simulated wafer image 118 in FIGS. 2A-2C) is determinedusing an optical path 342 having a suitably illuminated input 340 (suchas the reconstructed photo-mask image 214 in FIGS. 2A-2C or acorresponding estimated photo-mask) at one of its object planes. In thiscase, the optical path 342 corresponds to the lithography simulator 116(FIGS. 2A-2C) and may have a different numerical aperture, differentillumination configuration, and/or a different wavelength(s) than thatused in the optical path 312 (FIG. 3A). Furthermore, in some embodimentsthe optical path 342 may include some or all of the aspects of thephotolithographic process, such as illumination settings, theelectromagnetics of the photo-mask, the stepper optics, etc. Note thatin some embodiments the lithography simulator 116 (FIGS. 2A-2C) alsoincludes a model of a photoresist used in a photolithographic process.And in some embodiments, the lithography simulator 116 (FIGS. 2A-2C)includes flare and/or etch effects.

In some embodiments the inverse optical calculation 300 and/or theforward optical calculation 330 include fewer or additional components,two or more components are combined into a single component, and/or aposition of one or more components may be changed. Note thatcalculations corresponding to one or more optical paths in an inverseoptical calculation and/or a forward optical calculation may beimplemented using Fourier-optical techniques. Furthermore, the opticalpaths in an inverse optical calculation and/or a forward opticalcalculation may include multiple models of optical paths, such as wheninspection images from two or more different optical-inspection devicesand/or wafer-imaging devices are used to determine a reconstructedimage. Also note that while optical path 312 and optical path 342 havebeen traversed in particular directions, each of these optical paths maybe traversed in either direction.

While these optical calculations and the image processing techniqueshave been discussed in the context of photo-mask inspection, thisapproach may be applied in wafer inspection, and in particular, topatterned-wafer inspection. This is illustrated in FIGS. 4A and 4B,which provide block diagrams of wafer-inspection systems 400 and 430 inaccordance with an embodiment of the present invention. After measuringthe printed-wafer image 126, a reconstruction calculator 410 maydetermine a reconstructed wafer image 412 based on the target pattern130 and the printed-wafer image 126. As described in FIG. 3A, thereconstruction calculator 410 may utilize an inverse opticalcalculation.

The reconstructed wafer image 412 may correct for deficiencies in theprinted-wafer image 126, such as defocus, aberrations, and/or lostinformation due to limitations of the wafer-imaging device 124. Sincethe reconstructed wafer image 412 is a more faithful or accuraterepresentation of the patterned information on the printed wafer 122,wafer qualifier 414 may be able to make more accurate qualificationdecisions, i.e., whether or not the printed wafer 122 is acceptable. Asillustrated in FIG. 4A, these qualification decisions may be based oncomparisons between the reconstructed wafer image 412 and the targetpattern 130. Alternatively, as illustrated in FIG. 4B, the comparisonmay utilize a reference reconstructed wafer image 442 that is determinedfrom a reference printed-wafer image 440. This reference printed-waferimage may be from at least a portion of a same wafer or a differentwafer.

During these comparisons, features in the reconstructed wafer image 412(such as those corresponding to defects in the printed wafer 122) may beidentified and the printed wafer 122 may be accepted (or not) based onat least a subset of the identified features. For example, the printedwafer 122 may be accepted or rejected based on a type, severity, and/ornumber of features or defects (such as 1, 2, 5, 10, 25, 50, 100, 250,500, and/or 1000 identified features or defects per wafer) that areidentified. In addition, the printed wafer 122 may be accepted orrejected based on an impact of such features or defects on yield. And insome embodiments, statistics based on the identified features or defectsare determined. These statistics may include types of features (such aspoint, line or critical dimension defects) that may be used to classifythe printed wafer 122 and/or revise a manufacturing process thatproduced the printed wafer 122.

In some embodiments the wafer inspection system 400 and/or the waferinspection system 430 include fewer or additional components, two ormore components are combined into a single component, and/or a positionof one or more components may be changed. Note that the wafer-imagereconstruction illustrated in FIGS. 4A and/or 4B may be applied in thephoto-mask inspection system 200 (FIG. 2A), the photo-mask inspectionsystem 230 (FIG. 2B), and/or the photo-mask inspection system 250 (FIG.2C).

We now discuss methods for determining such reconstructed images. FIG.5A provides a flow chart illustrating a process 500 for determining animage in accordance with an embodiment of the present invention. Duringthis process 500, the system receives a mask pattern (510) and a firstimage of at least a portion of a photo-mask that corresponds to the maskpattern (512). The system determines a second image of at least theportion of the photo-mask based on the mask pattern and the first image(514). This second image is characterized by additional spatialfrequencies (i.e., it includes additional magnitude and/or phaseinformation at one or more additional spatial frequencies) than thefirst image. Then the system optionally calculates an estimated waferimage or pattern that results from a photo-lithographic process using anestimated photo-mask that corresponds to the second image (516).Furthermore, the system identifies features in the second imagecorresponding to differences between at least the portion of thephoto-mask and the mask pattern (518), and the system determines anacceptance condition of the photo-mask based on at least a subset ofthese features (520).

FIG. 5B provides a flow chart illustrating a process 530 for determiningan image in accordance with an embodiment of the present invention.During this process 530, the system receives a target pattern (540) anda first image of at least a portion of a patterned wafer thatcorresponds to the target pattern (542). The system determines a secondimage of at least the portion of the patterned wafer based on the targetpattern and the first image (544). This second image is characterized byadditional spatial frequencies (i.e., it includes additional magnitudeand/or phase information at one or more additional spatial frequencies)than the first image. Furthermore, the system identifies features in thesecond image corresponding to differences between at least the portionof the patterned wafer and the target pattern (546), and the systemdetermines an acceptance condition of the patterned wafer based on atleast a subset of these features (548).

Note that in some embodiments of the process 500 (FIG. 5A) and/or theprocess 530 there may be additional or fewer operations, the order ofthe operations may be changed, and two or more operations may becombined into a single operation. For example, the calculation (516 inFIG. 5A) may be performed for a variety of scenarios, including out offocus conditions, dose variations, etc., and features in one or more ofthe associated second images (i.e., the reconstructed images) may beidentified (518 in FIG. 5A) based on the estimated wafer patterns orsimulated wafer images that are calculated. In this way, it would bepossible to determine that a particular defect is fatal when slightlyoverexposed, even though it is negligible at the nominal dose.

In addition, in some embodiments the determining (514 in FIG. 5A) andidentifying (518 in FIG. 5A) operations are repeated iteratively, and atleast the subset of the features identified have a probability ofoccurrence that exceeds a pre-determined value. For example, asdiscussed below the features identified in a series of iterations may bethe best approximation to one or more first images (i.e., based on acomparison with projection of the corresponding one or morereconstructed images through a model of the optical path).Alternatively, the features identified may be those that result in theworst-case estimated wafer pattern or simulated wafer image.Furthermore, at least some of the identified features (such as adeviation in geometric position of a line edge in the estimated waferpattern) may be multiplied by a factor (such as 2×) to ensure that theresults are conservative. And in some embodiments, the featuresidentified may correspond to multiple simulations that have errorfunctions that are within an order of magnitude difference relative tothe simulation with the best approximation to the first image (i.e., thesimulation with a reconstructed image that, when projected through amodel of the optical path, is the best approximation to the firstimage).

Furthermore, in some embodiments acceptance of a photo-mask and/or apatterned wafer may be fully automated, while in other embodiments itmay not be filly automated. Thus, information may be presented to auser, who may verify an acceptance recommendation made by the system orwho may independently determine whether or not to accept the photo-maskand/or the patterned wafer. For example, if a confidence metric for theresults is less than a pre-determined value (such as when there are twovery different reconstructed images that each correspond to a similarvalue of the error function H), the user may be consulted to make afinal decision or judgment. In these embodiments, a ranking (such as atop-N list) of at least the subset of identified features may bepresented to the user. This ranking may indicate which features ordefects are deemed to be the most serious using comparisons of simulatedwafer images and target patterns, comparisons of simulated wafer imagesthat are determined using an estimated photo-mask (corresponding to thereconstructed photo-mask image) and the (target) mask pattern,comparisons of reconstructed images and target patterns or maskpatterns, a pre-determined set of features (known defects havingpre-determined sizes and/or phases), and/or statistics for thepre-determined set of features (such as their probabilities ofoccurrence). The user may observe the borderline cases. To assist theuser in this process, in some embodiments reconstructed images and/orsimulated wafer images may also be presented to the user. This approachmay allow the user to identify real defects that result in reducedprocess windows and lower yield at the wafer level, while ignoring falsedefects that may cause the mask shop to erroneously scrap or rework goodphoto-masks or the integrated-circuit manufacturer to discard apatterned wafer.

It will be recognized by one of ordinary skill in the art that theinverse optical calculation 300 described above in FIG. 3A is illdefined. In particular, numerous possible reconstructed images mayresult in the same observed inspection image 114 (FIGS. 2A-2C) orprinted wafer image 126 (FIGS. 2A, 4A and 4B). Therefore, as noted abovethe reconstructed image may be selected such that it is ‘most likely’ torepresent the actual photo-mask or the actual patterned wafer. A varietyof constraints and additional criteria may be imposed when determiningthe solution(s) to this problem in order to find a unique answer(s). Forexample, reconstructed images that, when projected through the opticalpath of the optical inspection device 112 (FIGS. 2A-2C) or thewafer-imaging device 124 (FIGS. 4A and 4B), correspond to inspectionimage 114 (FIGS. 2A-2C) or the printed-wafer image 126 (FIGS. 2A, 4A and4B) are more likely to represent the actual photo-mask or patternedwafer than other reconstructed images (i.e., has the smallest value ofthe error function).

Since defects are not part of the design data (i.e., the mask pattern orthe target pattern), a certain degree of ambiguity will also exist whendetermining the exact geometric configurations and phases of thedefects. Using a dark-field image as an example, in the limit of verysmall defects below the resolution limit of the optical-inspectiondevice 112 (FIGS. 2A-2C) or wafer-imaging device 124 (FIGS. 2A, 4A, and4B), the defects may be imaged as small gray dots. The amount of lighttransmitted by such defects may provide an indication of the defectsize, but approximately the same amount of transmission may be achievedby a more opaque defect of a larger size or by a more transparent defectof a smaller size.

It is possible to resolve some of this uncertainty as to the exactnature of the defect by collecting inspection images or printed-waferimages at multiple focus settings and programming the inverse opticalcalculation to determine the optimum photo-mask or wafer pattern thatwould most closely replicate the measured defects as a function offocus. In addition, the ambiguity may be resolved by optimizing overseveral optical paths, including several illumination configurations foreach path (thus, in general, multiple inspection images may be used,including images from different optical-inspection devices and/orwafer-imaging devices). For example, a transmitting defect on thesurface of a chromium-on-glass photo-mask that results in a phase shiftmay be determined. In addition, other parameters of theoptical-inspection device 112 (FIGS. 2A-2C) or wafer-imaging device 124(FIGS. 2A, 4A, and 4B) may be varied or modified, including theillumination and projection optics configurations, in order to produceinspection images or printed-wafer images that may be used in theinverse optical calculation. In all combinations of such conditions, thegoal of the inversion optical calculation is to find the unique solutionthat simultaneously minimizes the difference between the measuredinspection images or the measured printed-wafer images and the imagesthat result when the reconstructed images are projected through theoptical path of the optical inspection device 112 (FIGS. 2A-2C) or thewafer-imaging device 124 (FIGS. 2A, 4A and 4B).

However, even with the use of multiple imaging conditions, someambiguity may still remain in determining the exact size, shape, phase,and/or attenuation of one or more of the defects. As noted previously,in some embodiments of photo-mask inspection, the reconstructed imagethat is used to determine (via a corresponding estimated photo-mask in aforward optical simulation) an estimated wafer pattern or simulatedwafer image may be that which, when projected through the optical path,is the closest match or one of the closest matches to the inspectionimage or the printed-wafer image. Furthermore, this reconstructedphoto-mask may also provide a worst-case estimate of the defects acrossthe process window.

Other constraints based on a priori knowledge of the photo-mask or wafermanufacturing process may also be applied to resolve the ambiguity amongseveral competing candidate defect possibilities. For example, there maybe a priori knowledge about typical defect types (including thedistribution of defect sizes and phases) that arise during thephoto-mask or patterned-wafer manufacturing process. In addition,information may also be obtained from neighboring defects on thephoto-mask or patterned wafer that is being inspected, or from previousphoto-masks or patterned wafers that were manufactured on the sameprocess line and inspected. For example, given the likelihood that pointdefects tend to be generated by common mechanisms, a common link betweenmore than one such defect may constrain the possible solution options inthe inverse optical calculations.

One common type of defect is known as a critical dimension (CD) defector a sizing error. This type of defect is not an isolated feature (i.e.,a feature where one does not belong), or a missing feature (i.e., whereone was expected), but rather an error in the dimension of the featurebeing patterned on the photo-mask or the patterned wafer. Given theoften blurry grayscale inspection images or printed-wafer images, it maybe difficult for a user or operator to resolve these defects manually(i.e., to identify the defects in the inspection images or printed-waferimages). In addition, the large mask error enhancement factors (MEEFs)of leading-edge lithographic processes makes it important to understandhow such observed CD defects on or in photo-masks impact wafermanufacturing (i.e., the printed wafer patterns). The present inventionis well suited to identifying and assessing the impact (i.e., thesignificance) of these and other defects in the photo-masks andpatterned wafers.

We now discuss example embodiments of an inverse optical calculation todetermine a reconstructed image. The inverse optical calculation may bebased on minimization of an error function (which is also sometimesreferred to as a cost function or a Hamiltonian function). Referring toFIGS. 2A-2C, during each iteration of the calculation the error functionmay be a function of the difference between an image that results whenthe reconstructed photo-mask image 214 (or the reconstructed wafer image412 in FIGS. 4A and 4B) is projected through the optical path of theoptical inspection device 112 (or the wafer-imaging device 124 in FIGS.4A and 4B) and the inspection image 114 (or the printed-wafer image 126in FIGS. 4A and 4B). In some embodiments, the reconstructed imageinitially corresponds to the mask pattern (or the target pattern), andas the calculation progresses this reconstructed image is allowed toevolve while the inspection image 114 (or the printed-wafer image 126 inFIGS. 4A and 4B) is held constant. Including multiple inspection images(or multiple printed-wafer images), in some embodiments the errorfunction (H) equals

${\sum\limits_{j = 1}^{N}{w_{j}{{I_{j} - I_{oj}}}^{n}}},$where I_(j) is the forward projection of the jth reconstructed image(out of N reconstructed images in this example) through the opticalpath, w_(j) is a corresponding weight, I_(oj) is the jth inspectionimage (or the jth printed-wafer image), and n is a power. Note that theerror function (H) approaches zero as I_(j) approaches I_(oj).

In an example embodiment, N is 3 and n is 2. The 3 inspection images (orprinted-wafer images) may be determined at 3 different focal planes (orfocus settings) in the optical-inspection device 112 (or wafer-imagingdevice 124 in FIGS. 2A, 4A, and 4B). For example, with a wavelength of260 nm, the focal planes may be at −600 nm (relative to nominal focus),at 0 nm (i.e., at nominal focus), and 600 nm (relative to nominalfocus). Alternatively or in addition, the 3 inspection images (orprinted-wafer images) may be determined at three different wavelengthsor imaging conditions. Furthermore, a corresponding set of weights{w_(j)} may be 1, 0.1, and 1.

In other embodiments, the weights are varied as the inverse opticalcalculation progresses and/or different weights are used for specificparts (or even pixels) of an image. For example, the weights may bedetermined based on the difference between I_(j) and I_(oj) at a givenstep in the calculation. This approach may exaggerate the features ordefects, especially when the calculation is close to a local or globalminimum and the error function (H) corresponds to small differences.Thus, in general the error function (H) may be expressed as a doubleintegral over the image area and there may be separate time-dependentweights for I_(j) and I_(oj). Furthermore, in some embodiments the errorfunction (H) is expressed as a relative difference between I_(j) andI_(oj) for at least a portion of the calculation as it progresses.

We now describe an example embodiment of the forward projection usedwhen determining the error function. For simplicity, coherentillumination of the estimated photo-mask is utilized. Furthermore, theelectric field falling upon the photo-mask is approximately constant.Thus, the clear regions of the photo-mask pass the light, while theopaque regions block the light. It follows that a scalar electric fieldE, just behind the photo-mask, may be expressed as

${{E\left( \overset{\rightarrow}{r} \right)} = \begin{Bmatrix}0 & {chrome} \\1 & {glass}\end{Bmatrix}},$where {right arrow over (r)}=(x, y) is a point on the (x,y) plane. Asdiscussed below with reference to FIG. 6, this representation of thephoto-mask may be re-expressed using a function φ (referred to as alevel-set function) having positive regions that indicate glass andnegative regions that indicate chrome. Furthermore, the level-setfunction may equal zero at the boundaries or contours of thephoto-mask). Therefore, the electric field E associated with thephoto-mask may be re-expressed as a function of this level-set function,i.e.,E({right arrow over (r)})=ĥ(φ(x,y)),where ĥ is the Heaviside function

${\hat{h}(x)} = {\begin{Bmatrix}1 & {x \geq 0} \\0 & {x < 0}\end{Bmatrix}.}$

Since an ideal diffraction limited lens acts as a low-pass filter, thismay be used as an approximation to the actual (almost but not quiteperfect) lens in the optical path of the optical-inspection device (inthis example). Mathematically, the action of the lens may be expressedasA({right arrow over (r)})=f ⁻¹(Ĉ(f(E({right arrow over (r)}))))where A({right arrow over (r)}) indicates the electric fielddistribution on the wafer, f indicates the Fourier transform, f⁻¹indicates the inverse Fourier transform, and Ĉ indicates the pupilcutoff function, which is zero for frequencies larger than a thresholddetermined by the numerical aperture of the lens, and one otherwise.Thus, the pupil function is

${{\hat{C}\left( {k_{x},k_{y}} \right)} = {{\hat{h}\left( {k_{{ma}\; x}^{2} - \left\lbrack {k_{x}^{2} + k_{y}^{2}} \right\rbrack} \right)} = \begin{Bmatrix}0 & {{k_{x}^{2} + k_{y}^{2}} \geq k_{{ma}\; x}^{2}} \\1 & {{k_{x}^{2} + k_{y}^{2}} < k_{{ma}\; x}^{2}}\end{Bmatrix}}},$wherein k_(x), k_(y) and k_(max) represent frequency coordinates inFourier space. Therefore, the inspection image (at the detector) issimply the square of the electric fieldI({right arrow over (r)})=|A({right arrow over (r)})|².Combining these two equations, we findF(φ(x, y))=(|f ⁻¹(Ĉ(f(ĥ(φ(x, y)))))|²).This is a self-contained formula for the image seen by theoptical-inspection device (or, in alternate example, by thewafer-imaging device).

Note that this is just one embodiment of the forward projector that canbe used within the scope of this invention, chosen by way of example dueto its relative simplicity. More sophisticated forward models also fallwithin the scope of the present invention. Such models may take intoaccount, by way of example but not limitation, various illuminationconditions (e.g., off-axis, incoherent), the actual electromagnetics ofthe light field interacting with the photo-mask, various types ofphoto-masks other than chrome on glass (e.g., attenuated phase shifting,strong phase shifting, other materials, etc.), the polarization of thelight field, the actual properties of the lens (such as aberrations),and/or the vector nature of the electromagnetic field as it propagatesthrough the optical path.

We now describe the level-set functions in more detail. In the inverseoptical calculation, the reconstruction image(s) being modified may berepresented as a function having a set of values that is larger thanthose in the inspection images or the printed-wafer images. As discussedpreviously, in one embodiment the function is a level-set function. Thisis illustrated in FIG. 6, which provides a mask pattern 600 andcorresponding level-set functions 614 in accordance with an embodimentof the present invention. The mask pattern 600 includes alternatingregions with glass (610-1) and chromium (610-2). Transitions from oneregion to another are characterized by a contour or an edge, such asedge 612. When viewed from a direction perpendicular to a plane of thephoto-mask, the edge 612 defines the mask pattern 600.

Level-set function 614-1 has two values 616. The edge 612 may correspondto a mid-point between these two values 616. In contrast, level-setfunction 614-2 has three values 618, and the edge 612 may correspond tovalue 618-2. While not illustrated in FIG. 6, the level-set functions614 extend into the plane of FIG. 6 (i.e., they are 3-dimensionfunctions). As is known to one of skill in the art, there are manyalternate level-set functions and/or configurations that may be used.For example, in some embodiments one or more separate level-setfunctions and/or separate images may be used for the features ordefects.

As illustrated by level-set function 614-2, in some embodiments thelevel-set function may be expressed as a signed distance functionrelative to the contour or edge 612 (i.e., the value of the level-setfunction in at least a region is a function of the distance from theedge 612). This formulation may allow effects that occur nearer to theedge 612 (such as CD defects) to be highlighted. However, since featuresor defects in photo-masks and patterned wafers may occur at randomlocations (including those far removed from the edge 612), the level-setfunction 616-1 may be useful in that it provides an equal weighting withrespect to the edge 612.

In some embodiments, during each iteration of the inverse opticalcalculation the level-set function corresponding to one of thereconstructed images being modified is updated according toφ_(i+1)=φ_(i) +Δt·∇(H),where φ_(i+1) is an updated version of the level-set function, φ_(i) isthe current version of the level-set function, Δt is a step size in thecalculation and ∇(H) is a gradient or a derivative of the errorfunction. In an example embodiment, ∇(H) is

${\frac{\delta\; H}{\delta\;\phi}}_{\varphi_{i}},$i.e., it is the Frechet derivative of the error function H. Furthermore,in some embodiments ∇(H) is the direction of steepest descent forminimizing or optimizing H by changing φ. Furthermore, in someembodiments a 1^(st) order and/or a 3^(rd) order Runge-Kutta method isused when updating φ_(i). In other embodiments, a Conjugate Gradienttechnique, a Levenberg-Marquardt technique, a Quasi-Newton technique,and/or a Simplex technique may be used.

At least some aspects of Simulated Annealing may be utilized in someembodiments of the inverse optical calculation. In particular, the errorfunction H may be allowed to increase during some steps as thecalculation evolves. In this way, the global minimum in themulti-dimensional space may be determined. Note that the size of thismulti-dimensional space a number of quantization levels to the power ofthe number of pixels in the reconstructed images. In an exampleembodiment, these images have at least 1 million pixels (for example,1024×1024).

In one embodiment, in any iteration of the calculation changes in φ thatdecrease or increase the error function up to 0.5% are performed. If alarger change will result (i.e., ΔH>0.5%), the step size Δt is decreasedby a factor that is at least greater than 1 and the change in φ isimplemented (or not) based on a probability and a value P given by

${\mathbb{e}}^{\frac{{- k}\; H_{i + 1}}{H_{i}}},$where H_(i+1) is the error function in the i+1^(th) iteration (if thechange in φ is implemented) and H_(i) is the error function in i^(th)iteration (note that the ratio of H_(i+1)/H_(i) equals 1+ΔH). In someembodiments k is 0.155. For example, if the value P is 0.3 and a randomnumber between 0 and 1 is less than P, the error function is increasedbefore proceeding. In this way, the inverse optical calculationinitially takes large steps and thereby explores the solution space.

Furthermore, in some embodiments, the inverse optical calculation isdivided into a series of overlapping sub-problems (also referred to aswork units) at least some of which are processed independently and/orconcurrently. These work units may be based on elements or structures(for example, repetitive structures) in the mask pattern, the targetpattern, and/or in one or more of the inspection images or printed-waferimages. In some embodiments, the works units are selected such thatthere is a probability exceeding a pre-defined value (i.e., a highprobability) that most if not all of the work units include at most onedefect (for example, the work units may be based on differences betweenan inspection image and a simulated inspection image that is determineusing a theoretical mask pattern). Furthermore, in some embodiments thework units may partially overlap neighboring work units. For example,the work units may be between 10,000 nm² and 100 μm² in size.

In some embodiments, the inverse optical calculation is run for 100,1000 or 10,000 iterations at which point the optimal solution has beendetermined. In other embodiments, the calculation is stopped based onconvergence criteria, such as oscillatory behavior, a relative and/orabsolute difference between the inspection images (or the printed-waferimages) and the images that result when the reconstructed images areprojected through the optical path of the optical inspection device 112(or the wafer-imaging device 124 in FIGS. 4A and 4B), the latest changeto the error function H, and/or the history of changes to the errorfunction H. For example, the relative difference may be less than 1%and/or the absolute difference may be 10 nm for a critical dimension of100 nm. Note that is some embodiments, the level-set function isre-distanced (i.e., restored to one having the distance functionproperty relative to the edge 612) at intermediate iterations during thecalculation. In an example embodiment, such re-distancing occurs atleast every 20 iterations (for example, every 14 iterations).

Using this inverse calculation approach, features smaller than thewavelength of the light source used to perform optical measurements orto print wafer patterns in a photolithographic process may bedetermined. For example, in simulations using a light source having awavelength of 260 nm, features and defects as small as (10 nm)² on apatterned wafer or as small as (40 nm)² on a photo-mask were determined.

FIG. 7 provides a block diagram illustrating a pre-processing image 710(i.e., an inspection image or a printed-wafer image) and apost-processing image 720 (i.e., a reconstructed photo-mask image or areconstructed wafer image) in accordance with an embodiment of thepresent invention. In the pre-processing image 710, a line 710 (such asa 160-nm wide feature on a photo-mask) may include a possible defect712. However, as noted previously, the defect may be obscured due to thelimitations of the optical measurement equipment. After performing theinverse optical calculation, line 730 in the post-processing image 720is well defined, allowing defect 732 (a 40-nm gap in the photo-mask) tobe identified. The pre-processing image 710 was simulated using a modelof the optical path that included disk illumination (sigma=0.75), anumerical aperture of 0.67, and a wavelength of 260 nm.

We now discuss computer systems for implementing image reconstructionand photo-mask and/or patterned wafer qualification. FIG. 8 provides ablock diagram illustrating a computer system 800 in accordance with anembodiment of the present invention. The computer system 800 includesone or more processors 810, a communication interface 812, a userinterface 814, and one or more signal lines 822 coupling thesecomponents together. Note that the one or more processing units 810 maysupport parallel processing and/or multi-threaded operation, thecommunication interface 812 may have a persistent communicationconnection, and the one or more signal lines 822 may constitute acommunication bus. Moreover, the user interface 814 may include adisplay 816, a keyboard 818, and/or a pointer 820, such as a mouse.

Memory 824 in the computer system 800 may include volatile memory and/ornon-volatile memory. More specifically, memory 824 may include ROM, RAM,EPROM, EEPROM, FLASH, one or more smart cards, one or more magnetic discstorage devices, and/or one or more optical storage devices. Memory 824may store an operating system 826 that includes procedures (or a set ofinstructions) for handling various basic system services for performinghardware dependent tasks. The memory 824 may also store procedures (or aset of instructions) in a communication module 828. The communicationprocedures may be used for communicating with one or more computersand/or servers, including computers and/or servers that are remotelylocated with respect to the computer system 800.

Memory 824 may also include multiple program modules (or a set ofinstructions), including a reconstruction module 830 (or a set ofinstructions) to determine reconstructed images, a lithography module832 (or a set of instructions) to simulate a photo-lithographic process,a feature identification module 834 (or a set of instructions) toidentify features 864 in reconstructed images, and/or a qualificationmodule 836 (or a set of instructions) to determine an acceptancecondition of one or more photo-masks and/or patterned wafers. Theacceptance condition may be based on one or more acceptance criteria 840(such as a number, type, and/or severity of defects corresponding to thefeatures 864).

Furthermore, memory 824 may include pre-processing images 842 andpost-processing images 846, i.e., images before and afterreconstruction. The reconstruction module 830 and/or the lithographymodule 832 may utilize one or more stored models of optical paths 848 inphoto-lithographic systems and/or optical-inspection devices. In someembodiments, the reconstruction module 830 may utilize optionally storedweights 844.

Memory 824 may include mask patterns 850 and/or circuit patterns 856(i.e., target patterns). The reconstruction module 830 may utilize oneor more of these patterns when reconstructing pre-processing images 842corresponding to photo-masks and/or patterned wafers. In addition,memory 824 may include estimated mask patterns 852 and/or estimatedcircuit patterns 858. The lithography module 832 may utilize theestimated mask patterns 852 (which correspond to post-processing images846) to determine the estimated circuit patterns 858.

Memory 824 may also include process window(s) 854 corresponding to theestimated mask patterns 852, pre-defined features 860, statistics 862corresponding to these pre-defined features 860, and/or rankings 866 ofthe identified features 864. The qualification module 836 may determinethe acceptance condition of one or more photo-masks and/or patternedwafers based on one or more of these items, as well as the features 864.

Instructions in the various modules in the memory 824 may be implementedin a high-level procedural language, an object-oriented programminglanguage, and/or in an assembly or machine language. The programminglanguage may be compiled or interpreted, i.e., configurable orconfigured to be executed by the one or more processing units 810.

In some embodiments, at least some of the information in memory 824 isencrypted. For example, the lithographic module 832 and/or its outputfiles (the estimated circuit patterns 856) may be encrypted so thatintegrated-circuit manufacturers are more willing to share thisinformation with photo-mask shops (where photo-mask inspection may beperformed). As discussed in FIG. 9, in an alternate approach thephoto-mask shop may send the photo-mask images (i.e., inspection images)to integrated-circuit manufacturers, who may perform wafer-patternsimulations for one or more devices and/or may determine photo-maskacceptance.

Although the computer system 800 is illustrated as having a number ofdiscrete items, FIG. 8 is intended to be a functional description of thevarious features that may be present in the computer system 800 ratherthan as a structural schematic of the embodiments described herein. Inpractice, and as recognized by those of ordinary skill in the art, thefunctions of the computer system 800 may be distributed over a largenumber of servers or computers, with various groups of the servers orcomputers performing particular subsets of the functions. In someembodiments, some or all of the functionality of the computer system 800may be implemented in one or more ASICs, one or more field programmablegate arrays (FGPGAs), and/or one or more digital signal processors(DSPs).

The computer system 800 may include fewer components or additionalcomponents, two or more components may be combined into a singlecomponent, and/or a position of one or more components may be changed.In some embodiments the functionality of the computer system 800 may beimplemented more in hardware and less in software, or less in hardwareand more in software, as is known in the art.

As discussed previously, at least a portion of the image processing andinspection technique described may be implemented at a remote location.We now discuss such a method. FIG. 9 provides a flow chart illustratinga process 900 for determining an image in accordance with an embodimentof the present invention. During this process 900, a local computer 910provides image(s) and/or pattern(s) (914), and a server computer 912receives them (916). The system reconstructs the image(s) (918) based onthe pattern(s) and image(s), and optionally simulates wafer images (920)and/or compares the image(s) to desired or target patterns (922).Furthermore, the system identifies features (924) and determines whetheror not the photo-mask or patterned wafer is acceptable (926). Then theserver computer 912 provides results (928) and the local computer 910receives them (930).

Note that the information and files communicated between the localcomputer 910 and the server computer 912 are of a sensitive nature. As aconsequence, in some embodiments a user of the local computer 910 mayprovide one or more security tokens, such as a PIN code, a user name,and/or a password, in order to use the image reconstruction and/orlithography simulation programs or rmodules, as well as to accessinformation stored on the server computer 912. In addition, in someembodiments the stored files or data structures, and/or datacommunicated over a network linking the local computer 910 and theserver computer 912 are encrypted.

Also note that in some embodiments of the process 900 there may beadditional or fewer operations, the order of the operations may bechanged, and two or more operations may be combined into a singleoperation. For example, image reconstruction (918) and/or determinationof the acceptance condition (926) may occur at the local computer 910.

The approach illustrated in the process 900 may allow photo-mask shopsand integrated-circuit manufacturers to work together to determinewhether or not a photo-mask is acceptable, or should be reworked orrejected. Historically, both parties have had reservations about such anarrangement. Mask shops may be reluctant since it places the ability toreject a photo-mask in the hands of the end user (the integrated-circuitmanufacturer), who may be cautious about accepting a photo-mask and maynot have a financial motivation to accept a photo-mask that is less thanoptimal. In particular, since there is no cost to the end user, anypotential defect may result in a photo-mask being rejected and thephoto-mask shop may be forced to rewrite the photo-mask at theirexpense.

The approach described above may help resolve this conflict by creatinga computational infrastructure that is agreed upon by both thephoto-mask shop and the integrated-circuit manufacturer. In embodimentswhere photo-mask acceptance is fully automated, a system such as thatillustrated by the server 910 may be installed at the integrated-circuitmanufacturer and images sent by the photo-mask shop may be processedwithout exposing the details of the integrated-circuit manufacturingprocess to the photo-mask maker and yet at the same time withoutexposing the photo-mask shop to the human judgment of theintegrated-circuit manufacturer in accepting or rejecting photo-masks.

Alternatively, the photo-mask shop may calculate the reconstructed maskimage based on the measurements from the photo-mask-inspection device.This reconstructed mask image may then be sent to the integrated-circuitmanufacturer, where simulations of wafer patterns under various processconditions may be performed. The results may be sent back to thephoto-mask shop, where they may be used to determine the disposition ofdefects (i.e., whether or not the photo-mask is acceptable). Therefore,the embodiments of the system and method described herein may beimplemented by the photo-mask shop and/or by the integrated-circuitmanufacturer.

We now discuss data structures that may be used in the computer system800 (FIG. 8). FIG. 10 provides a block diagram illustrating an imagedata structure 1000 in accordance with an embodiment of the presentinvention. This data structure 1000 may include informationcorresponding to one or more images 1010. For a given image, such as theimage 1010-1, the data structure 1000 may include a focal plane or focuscondition 1012-1 at which the image was acquired, a wavelength at whichthe image was measured 1014-1, magnitude 1016-1 and/or phase 1018-1information.

FIG. 11 provides a block diagram illustrating a feature data structure1100 in accordance with an embodiment of the present invention. Thisdata structure 1100 may include information corresponding to one or morepre-defined features 1110. For a given feature, such as the feature1110-1, the data structure 1100 may include characteristics 1112-1 ofthe feature 1110-1 and/or an associated probability 1114-1 ofoccurrence. Note that that in some embodiments of the data structures1000 and/or 1100 there may be fewer or additional components, two ormore components may be combined into a single component, and/or aposition of one or more components is changed. For example, datastructure 1000 may include information about the type of illumination(such as disk, point, annulus, sigmas, etc.) and/or details of theoptics (such as one or more wavelengths used or the numerical aperture).

While the preceding discussion has focused on techniques for inspectingphoto-masks and/or patterned wafers, these techniques may also be usedduring metrology, such as process development, process characterization,and/or process monitoring. For example, a calculation (such as aninverse optical calculation) may be used to deconvolve the effect on animage of an optical path in a metrology device. Note that in someembodiments the optical path includes immersion optics. Thus, one ormore of the techniques described previously may be used to enhance theresolution or recover additional information (such as spatialfrequencies) in an image of a patterned wafer and/or a photo-mask.

Note that these techniques may allow faster, cheaper, and/ornon-destructive measurements. For example, critical dimensions (CDs) ona patterned wafer may be determined using an optical microscope (asopposed to a scanning electron microscope). These CDs may be used tocalibrate design tools or modules (such as those for optical proximitycorrection) and/or manufacturing processes. Moreover, theseimage-processing techniques may be applied to measurements of isolatedfeatures (such as a line) and/or two-dimensional images.

In some embodiments, the image-processing techniques are used fordisposition analysis and/or defect review during development (as opposedto the defect inspection and review embodiments described previously).

Moreover, while the preceding discussion has used patterned wafers andphoto-masks as illustrative examples, the image-processing techniquesmay be used in a wide variety of imaging and/or measurement applicationswhich are based on wave phenomena propagating in different types ofmedia (such as electromagnetic waves and sound waves) and at differentranges of wavelengths (such as audio, radio, microwave, infrared,visible, ultra violet, and x-ray).

The foregoing descriptions of embodiments of the present invention havebeen presented for purposes of illustration and description only. Theyare not intended to be exhaustive or to limit the present invention tothe forms disclosed. Accordingly, many modifications and variations willbe apparent to practitioners skilled in the art. Additionally, the abovedisclosure is not intended to limit the present invention. The scope ofthe present invention is defined by the appended claims.

1. A method for inspecting a photo-mask, comprising: receiving aninspection image corresponding to the photo-mask, wherein the inspectionimage is determined using an optical imaging system; and iterativelyreconstructing an estimated pattern corresponding to the photo-mask atan object plane of the optical imaging system, thereby restoring imageinformation that was lost when the inspection image was determined,wherein the estimated pattern is determined using an inverse opticalcalculation in which the inspection image is in an image plane of theoptical imaging system and the estimated pattern is at the object planeof the optical imaging system.
 2. The method of claim 1, wherein theimage information was lost because of a transfer function of the opticalimaging system; and wherein the image information includes a spatialfrequency in a band of frequencies that is outside of a passband offrequencies associated with the transfer function.
 3. The method ofclaim 2, wherein the image information was lost because of a transferfunction of the optical imaging system; and wherein the estimatedpattern corrects for distortion in the inspection image associated withthe transfer function.
 4. The method of claim 3, wherein the distortionincludes changes in an amplitude and a phase in the inspection image ata spatial frequency.
 5. The method of claim 1, wherein the iterativereconstructing is based on a mask pattern to which the photo-maskcorresponds.
 6. The method of claim 1, wherein the image informationincludes a spatial frequency in a band of frequencies that is outside ofa band of frequencies associated with the inspection image.
 7. Themethod of claim 1, further comprising identifying features in theestimated pattern corresponding to differences between the photo-maskand a mask pattern to which the photo-mask corresponds.
 8. The method ofclaim 7, further comprising determining an acceptance condition of thephoto-mask based on at least a subset of the features.
 9. The method ofclaim 8, wherein the acceptance condition is based on a number offeatures in at least the subset of the features.
 10. The method of claim8, wherein at least a subset of the features is identified based on anestimated wafer pattern that results from a photolithographic processusing the estimated pattern.
 11. The method of claim 10, wherein theestimated wafer pattern is calculated using a model of an optical pathused in the photolithographic process.
 12. The method of claim 11,wherein the model of the optical path includes a forward opticalcalculation in which the estimated pattern is included in an objectplane to determine the estimated wafer pattern.
 13. The method of claim11, wherein the estimated wafer pattern is calculated using a model of aphotoresist used in the photolithographic process.
 14. The method ofclaim 10, wherein at least the subset of the features is identifiedbased on differences between the estimated wafer pattern and a targetpattern, wherein the target pattern corresponds to at least a portion ofan integrated circuit.
 15. The method of claim 10, wherein an acceptancecondition of the photo-mask is determined based on a process windowcorresponding to the photolithographic process.
 16. The method of claim8, further comprising providing a ranking of at least the subset of thefeatures.
 17. The method of claim 8, wherein at least the subset of thefeatures correspond to potential defects in the photo-mask.
 18. Acomputer-program product for use in conjunction with a computer system,the computer-program product comprising a computer-readable storagemedium and a computer-program mechanism embedded therein for inspectinga photo-mask, the computer-program mechanism including: instructions forreceiving an inspection image corresponding to the photo-mask, whereinthe inspection image is determined using an optical imaging system; andinstructions for iteratively reconstructing an estimated patterncorresponding to the photo-mask at an object plane of the opticalimaging system, thereby restoring image information that was lost whenthe inspection image was determined, wherein the estimated pattern isdetermined using an inverse optical calculation in which the inspectionimage is in an image plane of the optical imaging system and theestimated pattern is at the object plane of the optical imaging system.19. A computer system, comprising: a processor; memory; and a programmodule, the program module stored in the memory and configured to beexecuted by the processor to inspect a photo-mask, the program moduleincluding: instructions for receiving an inspection image correspondingto the photo-mask, wherein the inspection image is determined using anoptical imaging system; and instructions for iteratively reconstructingan estimated pattern corresponding to the photo-mask at an object planeof the optical imaging system, thereby restoring image information thatwas lost when the inspection image was determined, wherein the estimatedpattern is determined using an inverse optical calculation in which theinspection image is in an image plane of the optical imaging system andthe estimated pattern is at the object plane of the optical imagingsystem.